It is a front wheel drive car, and therefore it does work differently vs. a rear wheel driver car.
You see FWD race car around the track and sometime you see the rear wheel lift off the ground, there is a reason for that.
One of the trick in building a good fast track FWD car is to limit rear compression travel.
That way when you brake and turn in, the rear damper top out.
This try to lift the rear wheel off the ground.
The reason for this is because you want keep that front wheel hook for as long as you can and put as much weight on it as possible, as that is the bit that is generating traction.
The only problem with this design is that you cannot really use this on a road car, as it would be pretty uncomfortable and dangerous in low grip surfaces (think cold wet morning in winter).
Of course there are other bits also, springs rate play a role, damper plays a role.
FWD car is an odd setup as a good fast road going setup isn't really optimal for track use.
Because for safety sake, you want the rear to grip harder than the front; if you are going to crash you want to front end to hit the wall instead of side way if that make sense.
However, for track use, you want that rear end to be loose so you can turn in, and that mean swapping the wheel frequency (springs rate) so the lower end is at the drive wheel.
Otherwise, the only other solution is like you say, tune tyre pressure, anti-roll bars, or just change your driving style with lift off over steer.
There are a lot of way to tune a car, the problem is the more "focus" you make it for one thing, the less it is able to do others.
If this is a trailered to track only car driven on slick, we can make a suspension that will work for that on the track, but it will try to kill you as soon as you hit some uneven country roads.
Jerrick